We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential α V. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.

Adami, R., Figari, R., Finco, D., & Teta, A. (2006). On the asymptotic dynamics of a quantum system composed by heavy and light particles. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 268(3), 819-852 [10.1007/s00220-006-0115-0].

On the asymptotic dynamics of a quantum system composed by heavy and light particles

ADAMI, RICCARDO;
2006

Abstract

We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential α V. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.
Articolo in rivista - Articolo scientifico
quantum mechanics, Schroedinger equation, decoherence, dispersive estimates
English
Adami, R., Figari, R., Finco, D., & Teta, A. (2006). On the asymptotic dynamics of a quantum system composed by heavy and light particles. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 268(3), 819-852 [10.1007/s00220-006-0115-0].
Adami, R; Figari, R; Finco, D; Teta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/5994
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